Elliptic curve search results

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
71.2-b1	71.2-b	$2$	$2$	6.6.300125.1	$6$	$[6, 0]$	71.2	\( 71 \)	\( -71 \)	$69.83308$	$(-2a^5+a^4+14a^3+4a^2-9a-4)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 1 \)	$0.003038782$	$267854.1885$	2.22863	\( -\frac{5033651}{71} a^{5} + \frac{1531845}{71} a^{4} + 506333 a^{3} + \frac{15162761}{71} a^{2} - \frac{22635572}{71} a - \frac{5576043}{71} \)	\( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( 4 a^{5} - 2 a^{4} - 28 a^{3} - 7 a^{2} + 18 a + 1\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 22 a^{5} - 4 a^{4} - 160 a^{3} - 84 a^{2} + 102 a + 36\) , \( 12 a^{5} - 4 a^{4} - 87 a^{3} - 34 a^{2} + 62 a + 16\bigr] \)	${y}^2+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-39a-12\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-7\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-28a^{3}-7a^{2}+18a+1\right){x}^{2}+\left(22a^{5}-4a^{4}-160a^{3}-84a^{2}+102a+36\right){x}+12a^{5}-4a^{4}-87a^{3}-34a^{2}+62a+16$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.